时间：2019年12月21日上午8:30-18:00

地点：数统楼213

报告一：陈建清（福建师范大学）

题目：包含卷积非线性的薛定鄂方程和方程组

摘要: 本报告首先介绍一些包含卷积非线性的薛定鄂方程解的存在性、多重性等结果；接着结合变分方法介绍单个薛定鄂方程的柯西问题解的存在性；最后介绍包含卷积非线性的薛定鄂方程组的柯西问题解的存在性。

报告二：王 俊（江苏大学）

题目：Existence and bifurcation of nontrivial solutions for the coupled nonlinear Schrodinger-Korteweg-de Vries system

摘要：In this talk, we consider the existence and bifurcation of nontrivial solutions of the nonlinear Schrodinger-Korteweg-de Vries(NLS-KdV) and Schrodinger-Korteweg-de Vries-Korteweg-de Vries(NLS-KdV-KdV) systems which arise from fluid mechanics. On the one hand, for both the three-wave system and two-wave system, the

existence/nonexistence, continuous dependence and asymptotic behavior of positive ground state solutions are established. On the other hand, multiple positive solutions are found via a combination of Nehari manifold and bifurcation methods for the attractive interaction case.

报告三：黄 锐（华南师范大学）

题目： Stability of traveling waves for time-delayed nonlocal dispersion equation

摘要：We will talk about the stability of traveling waves for time-delayed nonlocal dispersion equation, including the monotone/non-monotone critical/non-critical traveling waves. Some numerical simulations will be also presented to confirm our theoretical results.

报告四：刘海东（嘉兴学院）

题目：A coupled Schrodinger system with critical exponent

摘要：

报告五：陈世炳（中国科学技术大学）

题目：Free boundary in optimal transport

摘要：Free boundary arises naturally in optimal transportation. The existence, uniqueness and $C^{1,\alpha}$ regularity were studied in a seminal paper by Caffarelli and McCann. In this talk, I will discuss some recent progress on this problem. This is based on a joint work with Jiakun Liu.

报告六：向长林（长江大学）

题目：Regularity theory for some higher order elliptic systems

摘要：In this talk, I will discuss a regularity problem of some higher order elliptic systems originated from geometry, including the fourth order elliptic system proposed by Lamm and RiviYre which models geometric objects such as biharmonic mappings between Riemannian manifolds. Lamm and RiviYre applied the method of conservation law to derive continuity of solutions. However, their approach is quite di_cult to be applied to higher order elliptic systems. We will introduce an elementary approach which is easy to be applied to higher order problems, and also is applicable to derie Holder continuity of solutions directly. This is a joint work with Chang-Yu Guo in EPFL.

报告七：邓圣兵 （西南大学）

题目： Bubble solutions for some Neumann problems in R^2

摘要：In this talk, I will present some results about the existence of bubble solutions for some Neumann problems in R^2, the problem has exponential nonlinratity term on the boundary condition.

报告八：张建军（重庆交通大学）

题目：Sign-changing solutions of nonlinear nonlocal problems

摘要：We are concerned with sign-changing solutions of nonlinear nonlocal elliptic problems, including Schrodinger-Poisson systems, Kirchhoff equations and gauged Schrodinger equations. By employing a novel perturbation approach and the method of invariant sets of descending flow, we prove that the problems above admit multiple sign-changing solutions.

报告九：王春花（华中师范大学）

题目：Multi-peak positive solutions to a class of Kirchhoff equations

摘要：In this talk, we consider a nonlocal Kirchhoff problem. Under some mild assumptions on the function V, we obtain multi-peak solutions for sufficiently small by Lyapunov-Schmidt reduction method. Even though many results on single peak solutions to singularly perturbed Kirchhoff problems have been derived in the literature by various methods, there exist no results on multi-peak solutions before our work, due to some difficulties caused by the nonlocal term. A remarkable new feature of this problem is that the corresponding unperturbed problem turns out to be a system of partial differential equations, but not a single Kirchhoff equation, which is quite different from most of elliptic singular perturbation problems. This is based on a joint work with Prof. S. Peng, P. Luo and C. Xiang.